Getal & Ruimte (12e editie) - vwo wiskunde B
'Rekenen met logaritmen'.
| vwo wiskunde B | 5.4 Logaritmen |
opgave 1Bereken. 1p a \({}^{2}\!\log(64)\) Logaritme (1) 00fi - Rekenen met logaritmen - basis - 0ms a \({}^{2}\!\log(64) = {}^{2}\!\log(2^{6}) = 6\) 1p 1p b \({}^{2}\!\log(2)\) Logaritme (2) 00fj - Rekenen met logaritmen - basis - 0ms b \({}^{2}\!\log(2) = {}^{2}\!\log(2^{1}) = 1\) 1p 1p c \(\log(10)\) Logaritme (3) 00fk - Rekenen met logaritmen - basis - 0ms c \(\log(10) = \log(10^{1}) = 1\) 1p 1p d \({}^{8}\!\log(\frac{1}{64})\) Logaritme (4) 00fl - Rekenen met logaritmen - basis - 0ms d \({}^{8}\!\log(\frac{1}{64}) = {}^{8}\!\log(8^{-2}) = -2\) 1p opgave 2Bereken. 1p a \({}^{\frac{1}{9}}\!\log(\frac{1}{81})\) Logaritme (5) 00fm - Rekenen met logaritmen - basis - 0ms a \({}^{\frac{1}{9}}\!\log(\frac{1}{81}) = {}^{\frac{1}{9}}\!\log(\frac{1}{9}^{2}) = 2\) 1p 1p b \({}^{\frac{1}{7}}\!\log(49)\) Logaritme (6) 00fn - Rekenen met logaritmen - basis - 0ms b \({}^{\frac{1}{7}}\!\log({}^{\frac{1}{7}}\!\log(49)) = {}^{\frac{1}{7}}\!\log(\frac{1}{7}^{-2}) = -2\) 1p 1p c \({}^{3}\!\log(81 \sqrt{3})\) Logaritme (7) 00fo - Rekenen met logaritmen - basis - 0ms c \({}^{3}\!\log(81 \sqrt{3}) = {}^{3}\!\log(3^{4} ⋅ 3^{\frac{1}{2}}) = {}^{3}\!\log(3^{4\frac{1}{2}}) = 4\frac{1}{2}\) 1p 1p d \({}^{7}\!\log(7^{4{,}7})\) Logaritme (8) 00fp - Rekenen met logaritmen - basis - 0ms d \({}^{7}\!\log(7^{4{,}7}) = 4{,}7\) 1p |